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# Communications in Number Theory and Physics

## Volume 11 (2017)

### Number 1

### Stringy Chern classes of singular toric varieties and their applications

Pages: 1 – 40

DOI: http://dx.doi.org/10.4310/CNTP.2017.v11.n1.a1

#### Authors

#### Abstract

Let $X$ be a normal projective $\mathbb{Q}$-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in $X$ via the total stringy Chern class of $X$. This formula is motivated by its applications to mirror symmetry for Calabi–Yau complete intersections in toric varieties.We compute stringy Chern classes and give a combinatorial interpretation of the stringy Libgober–Wood identity for arbitrary projective $\mathbb{Q}$-Gorenstein toric varieties. As an application we derive a new combinatorial identity relating $d$-dimensional reflexive polytopes to the number $12$ in dimension $d \geq 4$.

Received 26 July 2016

Published 16 June 2017